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Solution Examples: A company issues $100,000 of 5 year bonds with a stated rate of 8%. Interest payments are made semiannually. Draw a timeline for each of the two cash flows: _______|_______|_______|_______|_______|_______|_______|_______|_______|_______| $100,000 _______|_______|_______|_______|_______|_______|_______|_______|_______|_______| $4,000 $4,000 $4,000 $4,000 $4,000 $4,000 $4,000 $4,000 $4,000 $4,000 Par Example (market rate = stated rate) A company issues $100,000 of 5 year bonds with a stated rate of 8% when the market rate of interest is 8%. Interest payments are made semiannually. What is the selling price (proceeds) of the bond issue? Market rate = 8%; Stated rate = 8% Selling price(proceeds): Present value of the principal +Present value of the interest payments per compound period Selling price of the bonds n = 5 years X 2 = 10 i = 8% ÷ 2 = 4% Interest payment per compound period: Face value X stated rate X time $100,000 X 8% X 6/12 = $4,000 OR $100,000 X 4% = $4,000 PV = FV(PVFSSn,i) = $100,000(PVFSS10,4%) = $100,000(.67556) = $67,556 +PV = R(PVFOAn,i) = $4,000(PVFOA10,4%) = $4,000(8.1109) = 32,444 (rounded) Selling price $100,000 Cash Bonds Payable 100,000 100,000 Solution 10-2 Par Premium example (market rate < stated rate) A company issues $100,000 of 5 year bonds with a stated rate of 8% when the market rate of interest is 6%. Interest payments are made semiannually. What is the selling price (proceeds) of the bond issue? Market rate = 6%; Stated rate = 8% Selling price(proceeds): Present value of the principal +Present value of the interest payments per compound period Selling price of the bonds n = 5 years X 2 = 10 i = 6% ÷ 2 = 3% Interest payment per compound period: Face value X stated rate X time $100,000 X 8% X 6/12 = $4,000 OR $100,000 X 4% = $4,000 PV = FV(PVFSSn,i) = $100,000(PVFSS10,3%) = $100,000(.74409) = $74,409 +PV = R(PVFOAn,i) = $4,000(PVFOA10,3%) = $4,000(8.5302) = 34,121(rounded) Selling price $108,530 Cash Bonds Payable Premium on Bonds Payable 108,530 100,000 8,530 Discount example (market rate > stated rate) A company issues $100,000 of 5 year bonds with a stated rate of 8% when the market rate of interest is 10%. Interest payments are made semiannually. What is the selling price (proceeds) of the bond issue? Market rate = 10%; Stated rate = 8% Selling price(proceeds): Present value of the principal +Present value of the interest payments per compound period Selling price of the bonds n = 5 years X 2 = 10 i = 10% ÷ 2 = 5% Interest payment per compound period: Face value X stated rate X time $100,000 X 8% X 6/12 = $4,000 OR $100,000 X 4% = $4,000 PV = FV(PVFSSn,i) = $100,000(PVFSS10,5%) = $100,000(.61391) = $61,391 +PV = R(PVFOAn,i) = $4,000(PVFOA10,5%) = $4,000(7.72173) = 30,887 (rounded) Selling price $92,278 Cash 92,278 Discount on Bonds Payable 7,722 Bonds Payable 100,000 Solution 10-3 Premium Solution 10-4 Discount